The biggest legal issue is the size/weight/caliber restrictions of different states. In Montana, there is no such restrictions. The only restrictions placed on the firearm you can use are pretty much limited to prohibiting poisonous, explosive, or non-expanding ammunition. But I recall some hunters in Wyoming shoot game at pretty long ranges with some heavy target rifles chambered for some hot .33 caliber wildcats, and the resulting limitations that state placed on weight limits for rifles the next season. I'd check local laws to be safe.
If there is no state laws prohibiting the use of such rifles, then the determining factor is whether you want to pack around a 30+ pound rifle, or put forth the time to learn how to estimate range, read wind, adjust your optics, and shoot at long range, so you can take advantage of the capabilities of the system.
The lack of appropriate ammunition should be considered in advance as well. Right now my brother is loading 750 gr Barnes Long Range Solids in his AR-50. This projectile would be illegal because it is non-expanding, and the law makes pays no regard to caliber or energy. The 750 gr Hornady Amax might work, but might also expand too fast, and there is no way to know for sure until you drop the hammer on a living creature. Whether you are okay taking the risk of wounding or maiming the animal you pursue is up to you, but most of us at least pretend to care about giving our quarry as respectful and humane a death as possible.
I am not saying I wouldn't hunt with a .50 BMG. I would just have to find what I deemed suitable ammunition first. That would be something that expands and still leaves something to eat. When I find such a thing, in fact, I will be using it to hunt with a .50. Until then, I'll have to stick to my 7 mm Rem Mag.